Even so, Mr. Zuma remained defiant, saying he had done nothing wrong, and had been “victimized” by party leaders.

Breaking his silence on the crisis in a live interview with the state broadcaster SABC, Mr. Zuma said that the effort to remove him was “unfair,” and that party officials had not given him a reason for their decision. “Nobody’s saying what I’ve done,” he said.

He said he would make a formal statement later on Wednesday.

Mr. Zuma has been found guilty of violating the Constitution in his handling of a corruption case related to his homestead, Nkandla. In addition, a public inquiry on widespread influence-peddling in his administration is expected to be held in the months ahead.

Political experts have pointed out that by vacating the presidency, Mr. Zuma would make himself vulnerable to pending inquiries and corruption charges from before he took office that he has been able to deflect as the president.

On Tuesday, the A.N.C. ordered Mr. Zuma to step down as South Africa’s leader, saying his continued presence would “erode the renewed hope and confidence among South Africans” since party elections in December, in which Mr. Ramaphosa defeated Mr. Zuma’s preferred candidate for the leadership of the A.N.C.

But party leaders did not elaborate on their decision to dismiss Mr. Zuma, even saying that ethical concerns had not been a consideration. They did not explain, as Mr. Zuma himself pointed out in the television interview, why they had loyally backed him until two months ago and were now demanding his resignation. What had changed, beyond the fact that there was now a new A.N.C. leader who wanted him out?

As Mr. Zuma remained silent on Wednesday morning, he came under new pressure to resign, as the police raided the residence in Johannesburg of the Guptas, a family with wide-ranging business interests and close ties to one of the president’s sons and his political allies. The Guptas have appeared to operate above the law under Mr. Zuma’s protection, but the police force’s investigative unit, which has long been subject to political interference, is now investigating the powerful family.

Local news outlets reported that three people, including a member of the family, had been arrested as part of a new police inquiry into influence-peddling.

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Police officers closed off roads around the Johannesburg home of the Gupta family, close allies of President Jacob Zuma of South Africa.Credit James Oatway/Reuters

Analysts said it was no coincidence that heavily armed police officers had raided the Guptas’ luxury compound and carried out arrests even as Mr. Zuma appeared to dither over whether to address the nation. The intended message, they said, was that those closest to Mr. Zuma, or even Mr. Zuma himself, could be next unless he acceded to the party’s order to quit, well before his term as president was scheduled to expire in mid-2019.

Around noon on Wednesday, as Mr. Zuma still gave no indication of speaking, party leaders held a news conference and announced they would move to remove him through a no-confidence vote the next day. They said they would work with an opposition party, the Economic Freedom Fighters, which had already pushed for a no-confidence vote in Parliament.

“The ball is in his court,” said Paul Mashatile, the A.N.C.’s treasurer general.

The fast-moving developments complicated efforts by Mr. Ramaphosa to achieve a smooth transfer of power that would avoid widening fissures inside the party.

The events were also a clear sign of how much has changed in the two months since Mr. Ramaphosa was chosen to succeed Mr. Zuma as the leader of the A.N.C., creating what South Africans refer to as the two centers of power — the presidency and the head of the party.

Mr. Zuma, seemingly untouchable just a couple of months ago, was pushed to a humiliating choice: Resign or be fired.

In the interview with SABC, which came after the announcement of the no-confidence vote, Mr. Zuma said he had offered to step down — though not until June. In the next months, he said, he needed to carry out certain duties, including introducing his successor, Mr. Ramaphosa, to other African heads of state at upcoming regional meetings.

“I should agree to resign, but let us work on a time frame,” he said he had told party officials during negotiations.

A.N.C. officials have said previously that Mr. Zuma had pressed to remain in office for another three to six months.

The A.N.C.’s difficult position was on clear display on Tuesday. At a news conference at its headquarters in Johannesburg, Ace Magashule — who is third in the party’s hierarchy and has traditionally acted as its spokesman — struggled to explain why the party was asking for Mr. Zuma’s resignation.

Mr. Magashule said the corruption accusations against the president had played no role, saying, “We did not take these decisions because Comrade Jacob Zuma has done anything wrong.”

Mr. Magashule’s remarks suggested the party might be reluctant to deal head-on with the culture of corruption that was endemic under Mr. Zuma.

The reason he gave for the party’s move was that Mr. Zuma’s continued presence as the nation’s leader would “erode the renewed hope and confidence among South Africans” since party elections in December.

Mr. Magashule indicated that Mr. Zuma was hurting the party’s electoral prospects, a point that Mr. Ramaphosa’s allies had emphasized.

In the 2016 local elections, the A.N.C. lost control over the nation’s biggest cities after it was deserted by traditional supporters disillusioned by Mr. Zuma’s conduct. Some party officials have since warned that it might face a similar fate in national elections in 2019.